Elementary Algebra

$n=-12$
Multiplying both sides by the $LCD= 4$ and then using the properties of equality, the value of the variable that satisfies the given equation, $\dfrac{2n+1}{4}+2=\dfrac{n-3}{4} ,$ is \begin{array}{l}\require{cancel} 1(2n+1)+4(2)=1(n-3) \\\\ 2n+1+8=n-3 \\\\ 2n-n=-3-1-8 \\\\ n=-12 .\end{array}